Building a Chess Board with Particles
The falling grid is quite easy to do with particles :

I forgot some things in the original answer, added them in emphasis


add a Grid object with 9x9 subdivisions (= 8x8 faces) (Not strictly necessary, a simple Plane works as well)
add a ParticleSystem on it with Grid distribution, render Unborn, Died, no Emitter. Choose a Grid Resolution of 8.
create a object for your tile, and add it as a Dupli Object for your Psys. Adjust his Size.
create a Plane somewhere under your emitter, and in Physics enable Collision ; check Kill Particles. 




The falling effect is working but all the tiles have the same color. To avoid that, you can give them a material like this one :



The Checker texture use the texture coordinates of the Grid object ; otherwise, the checker will apply on each individual Tile object.

The mapping node "kills" the Z component of the coordinates ; otherwise, the tiles will change color while falling (as their Z coordinate changes). Change X and Y Scale to 0.8 match the pattern of the tiles